Answer:
x-intercepts: (1,0), (-1,0)
y-intercept: (0,2), (0,-2)
Step-by-step explanation:
We are given the following in the equation:
[tex]4x^2+y^2 = 4[/tex]
x-intercept:
It is the value of x for which y is zero.
[tex]4x^2 + (0)^2 = 4\\4x^2 = 4\\x^2 = 1\\x = \pm 1[/tex]
x-intercepts: (1,0), (-1,0)
y-intercept:
It is the value of y for which x i 0.
[tex]4(0)^2 + y^2 = 4\\y^2 = 4\\y = \pm 2[/tex]
y-intercept: (0,2), (0,-2)
Symmetry around y-axis:
[tex]4(-x)^2 + y^2 =4 \\4x^2 + y^2 = 4[/tex]
Thus, it is symmetric around y-axis.
Symmetry around x-axis:
[tex]4x^2 + (-y)^2 = 4\\4x^2 + y^2 = 4[/tex]
Thus, it is symmetric around x-axis.
Symmetry around origin:
[tex]4(-x)^2 + (-y)^2 = 4\\4x^2 + y^2 = 4[/tex]
Thus, it is symmetric around origin.
